# Properties

 Genus $$8$$ Quotient Genus $$0$$ Group $$C_2.S_4$$ Signature $$[ 0; 3, 4, 8 ]$$ Generating Vectors $$1$$

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## Family Information

 Genus: 8 Quotient Genus: 0 Group name: $C_2.S_4$ Group identifier: [48,28] Signature: $[ 0; 3, 4, 8 ]$
 Conjugacy classes for this refined passport: 3, 5, 7

 Jacobian variety group algebra decomposition: $A_{4}\times A_{2}^{2}$ Corresponding character(s): 4, 8

## Other Data

 Hyperelliptic curve(s): Yes Hyperelliptic involution: (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) (17,18) (19,20) (21,22) (23,24) (25,26) (27,28) (29,30) (31,32) (33,34) (35,36) (37,38) (39,40) (41,42) (43,44) (45,46) (47,48) Cyclic trigonal curve(s): No

 Equation(s) of curve(s) in this refined passport:
 $y^2=x(x^4-1)(x^{12}-33x^8-33x^4+1)$

## Generating Vector(s)

Displaying the unique generating vector for this refined passport.

8.48-28.0.3-4-8.1.1

 (1,9,17) (2,10,18) (3,15,22) (4,16,21) (5,12,24) (6,11,23) (7,14,19) (8,13,20) (25,33,41) (26,34,42) (27,39,46) (28,40,45) (29,36,48) (30,35,47) (31,38,43) (32,37,44) (1,31,2,32) (3,28,4,27) (5,29,6,30) (7,25,8,26) (9,47,10,48) (11,44,12,43) (13,45,14,46) (15,41,16,42) (17,39,18,40) (19,36,20,35) (21,37,22,38) (23,33,24,34) (1,44,6,48,2,43,5,47) (3,46,7,42,4,45,8,41) (9,36,14,40,10,35,13,39) (11,38,15,34,12,37,16,33) (17,28,22,32,18,27,21,31) (19,30,23,26,20,29,24,25)